Determine the intercepts of the line. $5x-9=-8y-3$ $x$ -intercept: $\Big($
Answer: The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $ \begin{aligned}5x-9&=-8\cdot{0}-3\\ 5x-9&=-3\\ 5x&=6\\ x&=1.2\end{aligned}$ So the $x$ -intercept is $\left(1.2,0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $ \begin{aligned}5\cdot0-9&=-8y-3\\ -9&=-8y-3\\ 8y&=6\\ y&=0.75\end{aligned}$ So the $y$ -intercept is $\left(0,0.75\right)$. In conclusion, The $x$ -intercept of the graph is $\left(1.2,0\right)$. The $y$ -intercept of the graph is $\left(0,0.75\right)$.